Problem: Simplify the following expression: $\sqrt{125} - \sqrt{45}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{125} - \sqrt{45}$ $= \sqrt{25 \cdot 5} - \sqrt{9 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{5} - \sqrt{9} \cdot \sqrt{5}$ $= 5\sqrt{5} - 3\sqrt{5}$ Finally, simplify by combining the terms. $= ( 5 - 3 )\sqrt{5} = 2\sqrt{5}$